Method of drilling a wellbore to a target

ABSTRACT

A method of drilling a wellbore to a target includes measuring attitudes at two adjacent survey stations along a wellbore using a downhole surveying tool. An actual change in wellbore position over a survey leg linking the two survey stations is determined. Corrections are applied to the measured attitude at one or both of the survey stations such that a modeled well path joining the survey stations reflects the determined actual change in wellbore positon between the two survey stations.

CROSS-REFERENCES TO RELATED APPLICATIONS

This application is a continuation application of and claims the benefitof priority of U.S. patent application Ser. No. 16/097,788 filed on Oct.30, 2018, entitled “METHOD OF DRILLING A WELLBORE TO A TARGET”, which isa U.S. national phase application and claims the benefit of priority ofapplication No. PCT/US2017/032295, filed on May 11, 2017, entitled“METHOD OF DRILLING A WELLBORE TO A TARGET”, which claims the benefit ofpriority to U.S. Provisional Application No. 62/408,622, filed on Oct.14, 2016, entitled “MEASUREMENT WHILE DRILLING METHOD”, and U.S.Provisional Application No. 62/335,078, filed on May 12, 2016, entitled“METHOD FOR CORRECTING POSITIONAL OR VERTICAL DEPTH ERRORS IN DOWNHOLEDIRECTIONAL SURVEYS”. Each of the foregoing applications in thisparagraph are incorporated herein by reference as if fully set forth intheir entireties for all purposes.

BACKGROUND OF THE INVENTION

In wellbore placement by measurement-while-drilling (MWD), surveys ofthe inclination and azimuth are taken at regular intervals along thewellbore. Industry standards require that a survey is taken at leastevery 100 feet. Commonly, a survey is taken every 90 feet, correspondingto the length of a “stand” consisting of three “singles” of drill pipe.In sections with strong curvature (“build-section”), it is common totake surveys every single of drill pipe (30 feet). The wellboretrajectory is then computed by minimum curvature interpolation, whichimplicitly assumes a circular arc (constant radial arc) between any twoadjacent survey stations. Since the true well path between adjacentsurvey stations is not usually a circular arc, the actual change inposition from one survey station to the next is different from thepositional change computed by minimum curvature. This problem is wellknown in the industry. It is a cause of considerable concern becauseeven small errors in vertical depth can lead to significant economiclosses due to stranded hydrocarbon resources. To avoid such errors,methods are available to measure or estimate the direction of thewellbore in the intervals between MWD surveys.

One method used to identify wellbore trajectory between MWD surveysincludes measuring the wellbore inclination and/or azimuth at manyadditional points between two stationary surveys. This is called“continuous survey” or “dynamic survey,” even though in practice it justemploys a higher sampling rate than the actual MWD survey stations.Continuous survey data may include inclination measurements only, orboth inclination and azimuth measurements. The wellbore trajectory isthen computed by minimum curvature interpolation that assumes a circulararc between any two adjacent points. The more additional data pointsthere are between the stationary surveys, the closer the two adjacentpoints, and the more accurate the computed wellbore trajectory betweenthe adjacent points may be. However, the use of additional intermediatedata points to facilitate better calculation of wellbore trajectoryintroduces operational complications in many workflows that usedirectional survey data.

BRIEF SUMMARY OF THE INVENTION

In one aspect, a method of drilling a wellbore to a target includesmeasuring attitudes at two adjacent survey stations along a wellboreusing a downhole surveying tool. The method further includes determiningan actual change in wellbore position over a survey leg linking the twoadjacent stations. Corrections are then applied to the measured attitudeat one or both of the survey stations such that a modeled well pathjoining the survey stations reflects the determined actual change inwellbore position between the two survey stations.

In another aspect, a method of drilling a wellbore to a target includesmeasuring attitudes at two adjacent survey stations along a wellboreusing a downhole surveying tool. The method further includes determiningan actual change in wellbore position over a survey leg linking the twoadjacent stations. Then, a notional survey station is interpolatedbetween the two adjacent survey stations. The interpolation involvescomputing the attitude of the notional survey station such that twomodeled well paths linking the two adjacent survey stations and notionalsurvey station reflect the determined actual change in wellbore positionover the survey leg.

In yet another aspect, a method of drilling a wellbore to a targetincludes measuring attitudes at least at two of consecutive first,second, and third survey stations along a wellbore using a downholesurveying tool. An actual change in wellbore position between the firstand third survey stations is determined. Then, corrections are appliedto the attitude of the second survey station such that two modeled wellpaths linking the three survey stations reflect the determined actualchange in wellbore position between the first and third survey stations.

BRIEF DESCRIPTION OF THE DRAWINGS

The following is a description of the figures in the accompanyingdrawings. The figures are not necessarily to scale, and certain figuresand certain views of the figures may be shown exaggerated in scale or inschematic in the interest of clarity and conciseness.

FIG. 1 shows a system for drilling a wellbore.

FIG. 2 shows a well path with survey stations.

FIG. 3A is a flowchart illustrating a method of drilling a wellbore to atarget, according to one embodiment.

FIG. 3B is a flowchart illustrating a method of drilling a wellbore to atarget, according to another embodiment.

FIG. 3C is a flowchart illustrating a method of drilling a wellbore to atarget, according to another embodiment.

FIG. 4A illustrates minimum curvature solution with standard survey.

FIG. 4B illustrates minimum curvature solution with corrected survey.

FIG. 5 illustrates a notional station interpolated between a previousand a current survey station.

FIG. 6 illustrates a notional station projected ahead of a currentsurvey station.

DETAILED DESCRIPTION OF THE INVENTION

Measurement-while-drilling (MWD) survey stations are typically spacedabout every 90 feet along the wellbore. Each MWD survey station ischaracterized by a measured depth, MD, inclination, Inc, and azimuth,Az. Inclination is the deviation of the wellbore from the vertical.Azimuth is the orientation of the wellbore relative to the north.Measured depth is the length of the wellbore. The survey data may berepresented by a set of direction vectors D in a North-East-Vertical(NEV) coordinate system. Each direction vector D corresponds to ameasured depth, MD, at a survey station and may be expressed as shown inEquation (1) below. (The direction vector D may also be described as theattitude of the corresponding survey station.)

D=|sin(Inc).cos(Az),sin(Inc).sin(Az),cos(Inc)|  (1)

where:

-   -   Inc=inclination    -   Az=azimuth    -   D=direction vector or attitude

The most widely used method for computing the well path in the industryis the minimum curvature method, which assumes a circular arc betweenany two adjacent survey stations with indices n−1 and n. The positioncoordinates of survey station n−1 are given or known. The positioncoordinates for survey station n, in terms of Easting, Northing, andTrue Vertical Depth, are calculated by fitting a circular arc to the twopositional vectors. If the well path between two adjacent surveystations n−1 and n is represented by position vectors P_(n−1) and P_(n),then

$\begin{matrix}{D_{n} = {❘{{{\sin\left( {Inc}_{n} \right)} \cdot {\cos\left( {Az_{n}} \right)}},{{\sin\left( {Inc}_{n} \right)} \cdot {\sin\left( {Az_{n}} \right)}},{\cos\left( {Inc}_{n} \right)}}❘}} & \left( {2A} \right)\end{matrix}$ $\begin{matrix}{{DL}_{n} = {\cos^{- 1}\left( {D_{n - 1} \cdot D_{n}} \right)}} & \left( {2B} \right)\end{matrix}$ $\begin{matrix}{P_{n} = {P_{n - 1} + {\left( {{MD_{n}} - {MD_{n - 1}}} \right) \cdot {\tan{{\left( \frac{DL_{n}}{2} \right)/{DL}_{n}} \cdot \left( {D_{n - 1} + D_{n}} \right)}}}}} & \left( {2C} \right)\end{matrix}$

where:

-   -   D_(n−1)=direction vector at survey station n−1    -   D_(n)=direction vector at survey station n    -   DL_(n)=dogleg angle between attitudes at survey stations n−1 and        n    -   MD_(n−1)=measured depth at survey station n−1    -   MD_(n)=measured depth at survey station n    -   P_(n−1)=position vector at survey station n−1    -   P_(n)=position vector at survey station n

In the case where DL_(n)=0, the expression tan(DL_(n)/2)/DL_(n) inEquation (2C) is replaced by ½.

The standard minimum curvature solution assumes that the entire intervalbetween survey stations n−1 and n will be drilled at a constant radiusof curvature. In reality, drilling of the interval will not follow acircular arc. In reality, the true changes in inclination and azimuthwill not be distributed along a circular arc over the survey intervalbetween the two adjacent survey stations. This means that the truechange in position between the survey stations will be different fromthe change in position computed by the minimum curvature method(Equations (2A) through (2C)). It is possible to estimate and correctthis positional error using additional information on the wellboretrajectory between surveys, such as through continuous surveying orslide sheets. However, in order for such a correction to beoperationally viable, it has to fit within the standard wellboresurveying framework that employs minimum curvature representation of thewellbore trajectory.

In one embodiment of the present disclosure, a method of correctingwellbore positional error includes applying corrections to the measuredattitude at one or both of two adjacent survey stations such that amodeled well path joining the two survey stations reflects the actualchange in wellbore position (usually expressed in 3 coordinates,Northing, Easting, and True Vertical Depth) between the two adjacentsurvey stations. Let the two adjacent survey stations be a previoussurvey station, n−1, and a current survey station, n. As the terms“previous” and “current” are used, the previous survey station will havea smaller measured depth (MD) compared to the current survey station.For this embodiment, the position vector, P_(n), at the current surveystation is estimated using additional survey information collectedbetween the previous survey station, n−1, and the current surveystation, n. Then, corrections to the attitude measured at the currentsurvey station are computed such that the minimum curvature solutionmatches the estimated position at the current survey station, n. This isin contrast to the standard minimum curvature computation usinguncorrected survey data, where the attitude at the current surveystation is matched but additional knowledge regarding the position ofthe current survey station is ignored. FIG. 4A illustrates a standardminimum curvature solution with uncorrected survey 400. The actual wellpath is shown at 402. Note the error 408 in true vertical depth (TVD)between the trajectory computed by the standard minimum curvaturesolution 400 and the actual well path 402 at the current survey station,n. FIG. 4B illustrates a minimum curvature solution with correctedsurvey 412, according to the present disclosure. The actual well path isshown at 402. Note that the corrected survey has eliminated the TVDerror at the current survey station, n, with the position of thewellbore trajectory computed by the minimum curvature solution matchingthe position of the actual well path at the current survey station, n.

For the embodiment described above, the modeled well path linking thetwo adjacent survey stations is described by Equations (3A) through(3C). Equation (3A) shows the direction vector, D_(n), at the currentsurvey station, n, with inclination correction, δInc_(n), to theinclination measured at the current survey station, n, and azimuthcorrection, δAz_(n), to the azimuth measured at the current surveystation, n. In alternate examples, only the measured inclination or onlythe measured azimuth may be corrected. The term “correction to attitude”will generally mean correction to one or both of the measuredinclination and azimuth. The dogleg angle, DL_(n), and position vector,P_(n), at the current survey station are given by Equations (3B) and(3C).

$\begin{matrix}{D_{n} = {❘{{{\sin\left( {{Inc}_{n} + {\delta{Inc}_{n}}} \right)} \cdot {\cos\left( {{Az_{n}} + {\delta Az_{n}}} \right)}}\ ,{{\sin\left( {{Inc}_{n} + {\delta{Inc}_{n}}} \right)} \cdot {\sin\left( {{Az_{n}} + {\delta Az_{n}}} \right)}}\ ,{\cos\left( {{Inc}_{n} + {\delta{Inc}_{n}}} \right)}}❘}} & \left( {3A} \right)\end{matrix}$ $\begin{matrix}{{DL}_{n} = {{\cos}^{- 1}\left( {D_{n - 1} \cdot D_{n}} \right.}} & \left( {3B} \right)\end{matrix}$ $\begin{matrix}{P_{n} = {P_{n - 1} + {\left( {{MD_{n}} - {MD_{n - 1}}} \right) \cdot {\tan{{\left( \frac{DL_{n}}{2} \right)/{DL}_{n}} \cdot \left( {D_{n - 1} + D_{n}} \right)}}}}} & \left( {3C} \right)\end{matrix}$

where:

-   -   Az_(n)=azimuth at current survey station    -   Inc_(n)=inclination at current survey station    -   δInc_(n)=correction to inclination at current survey station    -   δAz_(n)=correction to azimuth at current survey station    -   D_(n−1)=direction vector, or attitude, at the previous survey        station    -   D_(n)=direction vector, or attitude, at the current survey        station    -   DL_(n)=dogleg angle between attitudes at the two survey stations    -   MD_(n−1)=measured depth at the previous survey station    -   MD_(n)=measured depth at the current survey station    -   P_(n−1)=position vector at previous survey station    -   P_(n)=position vector at the current survey station

In the correction in FIG. 4B, note that the well-path vector 410 is nottangent to curve 412 at station n. This is because the correctiondefines a new survey vector that is tangent to the desired curve, but isnot necessarily aligned with the well path. Relaxing this tangentrestriction enables proper placement of the well using the circular arc.However, there is value in having the well path close to the tangentlines of the modeled curve 412. The embodiments described below use dualarc optimization to achieve this.

In another embodiment of the present disclosure, a method of correctingwellbore positional error includes applying corrections to the attitudeat a notional station interpolated between two adjacent survey stationssuch that two modeled well paths joining the notional station to each ofthe two adjacent survey stations reflect the actual change in wellboreposition between the two adjacent survey stations. For this embodiment,it is helpful first to consider the effect of interpolating a notionalstation between two adjacent survey stations, i.e., a previous surveystation, n−1, and a current survey station, n, and modeling the intervalbetween the two adjacent survey stations as two circular arcs. If theattitude of the interpolated notional station matches the attitude ofthe single circular arc linking the two adjacent survey stations, thenthe final position computed as two circular arcs remains unchanged. Ifthe attitude of the interpolated notional station is changed slightly upor down, left or right, then the final position of the current surveystation, n, computed from two circular arcs moves in the same direction.Thus, by selecting the correct attitude for the interpolated notionalstation, the position of the current survey station, n, as computed bytwo circular arcs can be made to closely match the estimated position atthe current survey station, n. As in the previous embodiment, theposition vector, P_(n), at the current survey station, n, can beestimated using additional survey information collected between theprevious survey station, n−1, and the current survey station, n.

For illustration purposes, FIG. 5 shows an example of a notionalstation, int, interpolated between two adjacent survey stations, n−1 andn. In FIG. 5, the curve 504 is tangent to (or defined by) the tangentlines defined by survey vectors (D) at stations int and n, and curve 502is tangent to (or defined by) the tangent lines defined by surveyvectors at stations int and n−1.

Suppose that the notional station, int, interpolated between twoadjacent survey stations is at a measured depth MD_(int) with attitudeD_(int) , then the two circular arcs (e.g., 502, 504 in FIG. 5) joiningthe adjacent survey stations to the notional station are solved by:

$\begin{matrix}{{DL}_{1} = {{\cos}^{- 1}\left( {D_{n - 1} \cdot D_{int}} \right)}} & \left( {4A} \right)\end{matrix}$ $\begin{matrix}{{DL}_{2} = {{\cos}^{- 1}\left( {D_{int} \cdot D_{n}} \right)}} & \left( {4B} \right)\end{matrix}$ $\begin{matrix}{P_{n} = {P_{n - 1} + {\left( {{MD_{int}} - {MD_{n - 1}}} \right) \cdot \frac{\tan\left( \frac{DL_{1}}{2} \right)}{DL_{1}} \cdot \left( {D_{n - 1} + D_{int}} \right)} + {\left( {{MD_{n}} - {MD_{int}}} \right) \cdot \frac{\tan\left( \frac{DL_{2}}{2} \right)}{DL_{2}} \cdot \ \left( {D_{int} + D_{n}} \right)} + {\Delta{{MD} \cdot D_{n}}}}} & \left( {4C} \right)\end{matrix}$

where:

-   -   DL₁=dogleg angle between attitudes at the previous survey        station and notional station    -   DL₂=dogleg angle between attitudes at the notional station and        current survey station    -   D_(n−1)=direction vector, or attitude, at the previous survey        station    -   D_(int)=direction vector, or attitude, at the notional station    -   D_(n)=direction vector, or attitude, at the current survey        station    -   MD_(n−1)=measured depth at the previous survey station    -   MD_(int)=measured depth at the notional station    -   MD_(n)=measured depth at the current survey station    -   ΔMD=residual error in along-hole depth    -   P_(n−1)=position vector at previous survey station    -   P_(n)=position vector at the current survey station

Since the final equation is in vector form, it provides three equations,which can be solved for ΔMD and D_(int). D_(int) is a unit vector withonly two independent unknowns, which can alternately be represented asInc_(int) and Az_(int). The position of MD_(int) would normally beselected to be midway between MD_(n−1) and MD_(n), in order to minimizethe curvatures of the segments. The mathematics can be made simpler anda non-iterative solution can be found, without significantly degradingaccuracy, by replacing each of the two expressions tan(DL/2)/DL with ½.

The embodiment described above may be used if it is acceptable to addinterpolated stations to the survey data or if it is acceptable toadjust the attitudes of alternate survey stations only. However, morecommonly the preferred solution adjusts the attitude of each surveystation in real time without adding additional stations.

In another embodiment of the present disclosure, a method of correctingwellbore positional error includes modeling the interval between threeconsecutive survey stations—a first station, n−1, a second station, n,and a third station, n+1 (where MD of the first station <MD of thesecond station <MD of the third station)—as two circular arcs, andapplying corrections to the attitude of the second station, n, such thatthe two circular arcs reflect the actual change in wellbore positionbetween the first station, n−1, and the third station, n+1. In oneexample, the stationary surveys at the three stations may be available,and the corrections to the second station may be determined using aprocedure similar to the one described above for the interpolatednotional station—in this case, the second station will correspond to theinterpolated notional station, the first station will correspond to theprevious station before the interpolated notional station, and the thirdstation will correspond to the current station after the interpolatednotational station. In another example, the calculation must be madeknowing the well path prior to the second (or current) station, n, to beadjusted, but without knowledge of the third (or next) station, n+1. Themost likely solution is therefore found by projecting the well pathahead to a notional station described by D_(n+1) and P_(n+1) inEquations (5A) and (5B), respectively, and adjusting the directionalvector D_(n) using the above technique over the three stations at n−1,n, and n+1. Note that Equation (5A) sets the directional vector at thenotional station (or third station), n+1, to be the same as thedirectional vector at the second station, n. In other examples, adifferent relationship between the directional vector at the notional(third) station and the second station may be used.

D _(n+1) =D _(n)   (5A)

P _(n+1) =P _(n)+(MD_(n)−MD_(n−1))·D _(n)   (5B)

where:

-   -   D_(n+1)=direction vector, or attitude, at the notional, or        third, station    -   D_(n)=direction vector, or attitude, at the second, or current,        station    -   P_(n)=position vector at the second, or current, station    -   P_(n+1)=position vector at the notional, or third, station    -   MD_(n)=measured depth at the second, or current, station    -   MD_(n−1)=measured depth at the first, or previous, station

In the example described above without knowledge of the third (or next)station, corrections may be applied to the current survey such thatcorrections needed to future surveys are minimized. In this case, thedistance of the wellbore ahead of the second station, n, has not beensurveyed yet, but it is possible to estimate the position of the nextstation (or third station) using secondary data, i.e., supplementalinformation that is outside of the stationary survey data (such asinformation from a qualitative orientation tool or sensor placed nearthe bit or information about how the well was directionally controlledduring the drilling, e.g., depths and toolface directions informationfrom slide sheets). This additional information can be used to create amore stable correction at the current station. Thus station “n−1” is theprevious (or first) survey station (used for the beginning of thetraditional minimum curvature calculation), station “n” is the current(or second) survey station (used as the end point for traditionalminimum curvature), and station “n+1 ” is next (or third) survey stationin the future whose position would have to be estimated. Byincorporating this information into the solution used at the second (orcurrent) survey station, n, the amount of correction that will be neededwhen the drill bit finally drills far enough to allow a stationarysurvey to be taken at the next survey station (n+1) will be reduced.Once the position of the notional future survey station (n+1) has beenestimated, then the minimum curvature solution will be similar to theprevious embodiment with three stations.

For illustration purposes, FIG. 6 shows a third station, n+1, projectedahead of a second (or current) station, n. The attitude of the secondstation, n, has been corrected such that the circular arcs (602, 604)linking the second station to the first (or previous) station, n−1, andthird station, n+1, reflect the estimated actual change in wellboreposition between the first and third stations. In FIG. 6, curve 604 istangent to (or defined by) the tangent lines defined by survey vectors(D) at stations n and n+1, and curve 602 is tangent to (or defined by)the tangent lines defined by survey vectors (D) at stations at n−1 andn.

FIG. 1 shows an example of a drilling environment in which theembodiments described above may be used. In the example drillingenvironment, a drill string 100 including a bottom hole assembly (BHA)102 is inserted through a wellhead 104 into a wellbore 106. The drillstring 100 may be supported by a derrick assembly 110, as is well knownin the art. The BHA 102 includes a drill bit 108 for drilling thewellbore 106. In one embodiment, the BHA 102 further includes ameasurements section 112, which includes sensors and other equipment formaking survey measurements from the wellbore 106. In one example, themeasurements section 112 may include one or more downhole surveyingtools, such as MWD module 114 and logging-while-drilling (LWD) module116. The measurements section 112 may further include an electronicsmodule 118, which may include a processor and other related computingdevices for processing and applying corrections to survey data downholeand storing data. The measurements section 112 may include acommunications module 120 for transmitting corrected and/or uncorrectedsurvey data to a recording unit 122 at the surface. The recording unit122 may be connected to appropriate computing facilities at the surfacethat allow processing of survey data received from the measurementssection 112. The electronics module 118 and communications module 120may be integrated into any or both of the measurement modules 114, 116.The BHA 102 may include other tools for directional drilling, such as arotary steerable system (RSS) 124. The RSS 124 may also include devicesfor making downhole measurements.

In accordance with the present disclosure, a method of drilling awellbore, such as wellbore 106, to a target involves making surveymeasurements along the wellbore. The survey measurements may be madeusing any known MWD and/or LWD techniques known in the art. The methodmay start at any point in the wellbore with a known position and a known(or assumed) orientation. For example, the starting point could be atthe wellhead, or at a kickoff point, i.e., where deflection of thewellbore from the vertical starts, or at the bottom of a casing in thewellbore, or at any other desired point in the wellbore with a knownposition. For illustration purposes, FIG. 2 shows an example well path200 from a wellhead A to a target B. The starting point, S₀, may be atthe wellhead A or at another point along the well path. Subsequentsurvey stations, S₁, S₂, . . . , S_(k-1), S_(k), are located along thewell path. The number of survey stations between the starting point, S₀,and the target B will depend on the length of the wellbore between thesepoints. The spacing between these survey stations will typically bearound 90 feet (equivalent to the length of three drill pipes), but maybe as small as 30 feet (equivalent to the length of a single drill pipe)in sections of the well path with strong curvature. The spacing betweensurvey stations may be coordinated with the length of the drill pipebecause stationary surveys can be taken when drilling is paused to allowaddition of drill pipes to the drill string in the wellbore. Suchstationary surveys are typically less noisy than surveys taken whiledrilling. The method may include drilling from one survey station to thenext and making a measurement at each survey station after suchdrilling. The method may also include making additional surveymeasurements while drilling from one survey station to the next. Themethod includes modifying the measured attitudes at survey stations toensure that modeled well paths between adjacent survey stations reflecttrue change in wellbore position between the adjacent survey stations,as described above. The method, as described herein, enables positionalaccuracy equivalent to the ones achievable by high-accuracy methods,such as described in the background, without the need to integratenumerous additional data into the survey record. The corrected attitudesmay be used to define the trajectory of the wellbore and enable accuratesteering of the wellbore to the target. Alternately, the correctedattitudes may be used for characterizing the well path after drilling.

FIG. 3A is a flowchart illustrating one practical implementation of amethod of drilling to a target according to the present disclosure. Theprocess may start at 300 at any point in the wellbore with a knownposition and a known (or assumed orientation). That known point whereeverything begins is the tie-in survey. The process may use an index nto keep track of the current survey station. In the next step 302, theindex n is incremented by 1, and a downhole surveying tool, e.g., MWDmodule 114 in FIG. 1, advances to the next survey station along thewellbore. In one embodiment, advancing the downhole surveying tool tothe next survey station may involve drilling the wellbore to the nextsurvey station. In the next step 304, a new survey measurement is madeat the current survey station n using the downhole surveying tool. Inthe next step 306, the actual change in position between the previoussurvey station, n−1, and the current survey station, n, is estimatedusing survey information available between the previous survey stationand the current survey station. Some examples of how the actual changecan be estimated will be discussed below. In the next step 308, attitudecorrections for the current survey leg are computed such that theminimum curvature trajectory from the previous survey station n−1 to thecurrent survey station n reflects the actual change in wellbore positionbetween the two stations. Variations to the workflow in FIG. 3A arepossible depending on the wellbore positional error correction methodused in the workflow. In general, any of the wellbore positional errorcorrection methods described above may be used. FIGS. 3B and 3C showexamples of variations to the workflow of FIG. 3A. In FIG. 3B, step 308B(corresponding to step 308 in FIG. 3A) is based on applying correctionsto a notional station interpolated between two survey stations. In FIG.3C, step 308C (corresponding to step 308 in FIG. 3A) is based onapplying corrections to the current survey station taking into account afuture survey station, and the preceding step 306C (corresponding tostep 306 in FIG. 3A) involves estimating an actual change in positionbetween the previous station and a future notional station determined byprojecting the wellbore path ahead of the current survey station.Another variant not shown in the drawings may involve repeating step 304such that three actual surveys are available as input for the wellborepositional error correction method in step 308C. That is, instead ofusing a future notional station, an actual third station where a surveymeasurement is taken using a downhole surveying tool may be used.

Returning to FIG. 3A, in the next step 310, the position of the currentsurvey station, n, is compared to the target to see if the drill bit isat the target. If the drill bit is not at the target, steps 302 to 310are repeated. In one embodiment, before repeating steps 302 to 310,steering parameters for a wellbore section to be drilled is determinedusing the corrected attitudes from step 308. As mentioned above, step302 may involve drilling the wellbore to the next survey station. Thecorrected attitudes of step 308 may be used to determine a wellboretrajectory that accounts for actual change in wellbore position betweensurvey stations, which can be used to make steering decisions whiledrilling the wellbore to the next survey station according to step 302.On the other hand, if the drill bit is at the target, the correctedprojection to bit, i.e., corrected distance to drill the bit from thecurrent survey station, is computed at 312. Corrected projection to bit,P_(bit), from the current survey station, n, can be computed byextrapolation as follows:

P _(bit) =P _(n)+DTB·D _(n)   (6)

where:

-   -   P_(bit)=corrected projection to bit    -   P_(n)=position vector at the current survey station n    -   DTB=distance from the surveying tool to the front of the drill        bit    -   D_(n)=direction vector, or attitude, at the current survey        station

The correction to bit is used to estimate the position of the hole thathas been drilled but where there might not be survey measurements. Dueto the presence of other drilling tools in the wellbore, the surveyinginstrument does not make it all the way down to the bottom of thewellbore. Therefore, it is necessary to estimate what the orientation ofthis final segment of the wellbore would be.

Steps 306 through 310 (or variants thereof) may be carried out in anappropriate module in the BHA, or parts or all of steps 306 through 310(or variants thereof) may be carried out with appropriate processingunit(s) or computer(s) at a surface location.

Determining Actual Change in Position Using Continuous Survey DataMethod

According to one embodiment, the actual change in position from theprevious survey station to the current survey station, n, in step 306may be estimated from continuous survey measurements. The continuoussurvey measurements are taken while drilling from the previous surveystation, n−1, to the current survey station, n. Although the survey isdescribed as continuous, in practice it just means that the continuoussurvey employs a higher sampling rate than the actual survey stations(or provides additional survey data points between the survey stations).The continuous survey is separate from the stationary (or static) surveymeasurements that are made at survey stations (step 304). The continuoussurvey measurements typically include measured depth, inclination, andazimuth data. The capability to make the continuous survey measurementsmay be provided by any suitable tool, such as a continuous inclinationsurvey tool, in the BHA.

For each survey interval from the previous survey station, n−1, to thecurrent survey station, n, the following information is needed:continuous inclination and/or azimuth sequence D(md_(m)), whereMD_(n−1)≤md_(m)≤MD_(n), m=1 . . . M, where MD is measurement depth. Tocompute the actual change in wellbore position, outliers from the Mvalues of D(md_(m)) are removed. Then, the corresponding change inposition from the previous station, n−1, to the current station, n, iscomputed. Data outliers can be removed by low-pass filtering,resampling, spline fitting, or by other means known in the art. Theoutput of this computation is the change in position from the previousstation, n−1, to the current station, n, denoted P_(n)-P_(n−1).

Pre-Processing of Continuous Survey Data

It should be noted that the continuous survey data may be subject toadditional error sources not present in stationary MWD survey. Vibrationduring the drilling process may introduce noise to the measurement. Inextreme cases, drilling tools such as agitators may be used thatintentionally induce axial vibrations by converting energy from mud flowinto linear motion. Single sensor readings will have increasedsusceptibility to residual calibration errors on the sensor being usedfor inclination measurements, as well as potential biases from assumedvalues of total gravity references. These error sources can causediscrepancies between the static MWD surveys and the data obtained viacontinuous inclination. To enable accurate estimation of the actualchange in position between two adjacent stations, it is necessary toprocess the continuous inclination data prior to its use in thecorrection method described above so that the benefits of includingadditional curvature in the survey are not outweighed by the detrimentsof including poor quality data.

In one embodiment, pre-processing of continuous survey data (measureddepth, inclination, azimuth) includes data conditioning, applyingadjustments to the depth data, and applying adjustments to thecontinuous orientation data.

Data Conditioning

In one embodiment, statistical outliers are removed from the continuoussurvey dataset. Noise-reduction functions are also applied to thedataset. This may include applying a smoothing function, resampling thedata at a more convenient rate for analysis, or creating synthetic dataas needed. The output of this step is a new continuous survey dataset(of the form measured depth, inclination, and azimuth) that is moreamenable to analysis.

Adjusting Depth Data

The measured depth data is adjusted to better correlate with thestationary survey depths. This process may include evaluating drillingparameters that can correlate sensor depth to survey depths (such as bitdepth, pump pressure, block position, and slide-rotate patterns), and itmay include looking at residuals when subtracting the stationary surveydata from the continuous survey data. These adjustments may be madeacross the entire dataset or across smaller subsets of the dataset assmall as a single point.

Adjusting Continuous Orientation Data

The continuous orientation data (inclination and azimuth) is adjusted tobetter correlate with the stationary survey depths. Where discrepanciesexist, the stationary survey will be assumed to be of superior qualityto the continuous data. For inclination, this may include calculating anoffset across the whole set or data or calculating multiple offsets tobe applied to subsets of data as small as individual points. For azimuthdata, the same treatment that is applied to the inclination data may beapplied or the azimuth may be replaced by taking interpolated azimuthsfrom the stationary survey set.

Determining Actual Change in Position between Stations Using Slide SheetMethod

A significant source of true vertical depth (TVD) errors is due to thewidespread use of mud motors in directional drilling. Mud motors makeuse of a bend in the BHA. Consider a bend that causes a wellborecurvature of 5 degrees per 100 feet. If the drill string is rotated, thebend rotates in all directions, resulting in a straight hole or a smallcurvature in a direction which results from gravity and the BHA design.If on the other hand the drill string does not rotate, but the motor isdriven by the mud flow, this results in a curve of 5 degrees per 100feet. By setting the orientation (“toolface”) of the bend, the curvatureof the wellbore can be oriented in the desired direction. In practice,this means that the wellbore is a sequence of “rotate” sections in whichthe direction is constant or slightly curved in a fixed direction andcurved “slide” sections in which the direction changes in the directionof the toolface setting. These alternating slide and rotate sections arenot accounted for in the standard minimum curvature representation ofthe wellbore trajectory.

According to the present disclosure, in another embodiment, for step306, the actual change in position from the previous survey station,n−1, to the current survey station, n, may be computed from slidesheets. A slide sheet is a record of whether the well was intentionallydeviated (“sliding” with a motor) or whether it was drilled with theassumption that the path would be straight (rotary drilling). By using arecord of the intended steering directions, the curvature of thewellbore between the stationary survey stations can be estimated.

For each survey interval from the previous survey station, n−1, to thecurrent survey station, the following information from the slide sheetsis needed: (1) “Slide” or “Rotate” mode for each segment of the intervaldrilled in a single mode; (2) the measured depths at each of the Mswitch-overs between slide and rotate segments for the interval,MD_(n−1)<md_(m)<MD_(n), m=1 . . . M, and (3) the toolface reported foreach “Slide” segment.

To compute the actual change in position, each sliding or rotatingsegment is modeled by a circular arc. Each circular arc is defined byits starting and ending depths MD_(m-1) and MD_(m), starting attitudeD_(m-1), starting toolface direction T_(m-1), and rate of curvatureC_(m). The ending attitude of a segment D_(m) can be computed fromEquations (7A) to (7C). The final direction vector D_(m) is found byrotation of the initial wellbore vector D_(m-1) and unit vector Y_(m-1)about the pole by angle R_(m).

R _(m) =C _(m)·(md_(m)−md_(m-1))  (7A)

Y _(m-1)=|cos(I _(m-1))·cos(A _(m-1))·cos(T _(m-1))−sin(A _(m-1))·sin(T_(m-1)),cos(I _(m-1))·sin(A _(m-1))·cos(T _(m-1)+cos() A _(m-1)).sin(T_(m-1)),−sin(I _(m-1))·cos(T _(m-1))|  (7)

D _(m) =D _(m-1)·cos(R _(m))+Y _(m-1)·sin(R _(m))  (7C)

where

-   -   R_(m)=rotation angle    -   C_(m)=rate of curvature    -   md_(m)=ending measured depth    -   md_(m-1)=starting measured depth    -   Y_(m-1)=unit vector normal to the initial wellbore vector Dm-1        and normal to the pole about which the wellbore interval curves    -   I_(m-1)=Starting inclination    -   A_(m-1)=Starting azimuth    -   T_(m-1)=starting toolface direction    -   D_(m)=ending attitude of a segment    -   D_(m-1)=starting attitude of a segment

Given values for each of the parameters, final direction vectors can befound for all of the segments within an interval by solving sequentiallyfrom the first segment to the last. Final position vectors P_(m) can beobtained by solving the circular arc formulas for each segment, the lastsuch vector giving the current position P_(n) at the end of theinterval.

Several different computation modes may be employed, depending on thenature of the survey interval.

Sliding Segments Only Mode

If the survey interval consists of a number of sliding segments but norotating segments, all of the depths and toolfaces are obtained fromslide sheet data. The only unknown is the rate of curvature C_(M), whichcan be assumed to be the same during each sliding segment. For anycurvature value C_(M), a solution can be found for the final attitudevector of the interval D_(M). The curvature value C_(M) which results ina final attitude vector closest to the measured attitude D_(n) at theend of the interval is taken to be the solution. The optimum value forC_(M) may be found by methods known in the art, such as Newton-Raphsoniteration.

Sliding and Rotating Segments Mode

If the survey interval contains both sliding and rotating segments, thecurvatures of each mode are unknown. It may be assumed that all slidingsegments have the same curvature C_(S), and all rotating segments havethe same curvature C_(R). If the rotating segments are assumed to havetoolface zero (rotating mode curvature is restricted to the verticalplane), the optimum values of C_(S) and C_(R) will match the finalattitude exactly. In this case the sliding mode matches all left/rightdeviation in the horizontal plane, and the rotating mode curvaturematches the residual up/down deviation in the vertical plane. As thecomputation is non-linear, iterative methods are again required to findthe solution.

If the rotating mode segments are allowed to deviate out of vertical,then the rotating mode toolface T_(R) represents a third unknown. Inthis case the problem cannot be solved using data from a single intervalor stand, as the final measured attitude provides only two independentequations. It can be solved using data from the current interval and theprevious interval, finding the parameters which best fit to bothmeasured attitudes D_(n−1) and D_(n).

For actively controlled steering tools which generate differentcurvatures in different segments within one interval, the ratio ofsegment curvatures should be provided (e.g., one segment at 50% andanother at 100%).

There are certain limitations to these techniques. If all slidingtoolfaces and rotating toolface coincide, it is not possible to find aunique solution. Under these circumstances one additional piece ofinformation must be provided, such as either the sliding or rotatingcurvature.

It should be noted that slide sheets report one toolface per segment. Asegment drilled with constant toolface does not generally follow acircular arc; however, the solutions provided above model each segmentas a circular arc defined by its initial toolface direction. In order tolimit systematic errors, the toolface reported on the slide sheet can beassigned to the midpoint of the corresponding circular arc. It is thenpossible to compute a starting toolface for use in the abovecalculations.

While the invention has been described with respect to a limited numberof embodiments, those skilled in the art of, having benefit of thisdisclosure, will appreciate that other embodiments can be devised whichdo not depart from the scope of the invention as disclosed herein.Accordingly, the scope of the invention should be limited only by theaccompanying claims.

What is claimed is:
 1. A method of drilling a wellbore to a target,comprising: receiving, from a computer system, attitudes at a firstsurvey station and a second survey station along a wellbore path using adownhole surveying tool, wherein the first survey station and the secondsurvey station are consecutive; modeling, by the computer system, basedon a first attitude of the wellbore at the first survey station, a firstinterval between the first survey station and the second survey stationas a first modeled well path; determining, by the computer system, basedon the first modeled well path, a first positional vector of thewellbore at the first survey station; modeling, by the computer system,based on a second attitude of the wellbore at the second survey station,a second interval between the second survey station and an estimatedposition of a third survey station as a second modeled well path;determining, by the computer system, based on the second modeled wellpath, a second positional vector of the wellbore at the second surveystation; and estimating, by the computer system, a position of the thirdsurvey station based on the first modeled well path, second modeled wellpath, first positional vector, and the second positional vector, whereinthe third survey station is beyond the second survey station along thewellbore path.
 2. The method of claim 1, wherein estimating the positionof the third survey station comprises determining a third attitude ofthe wellbore at the third survey station.
 3. The method of claim 2,wherein determining the third attitude of the wellbore at the thirdsurvey station comprises setting the third attitude to be the same as asecond attitude of the wellbore at the second survey station.
 4. Themethod of claim 1, the method further comprising: drilling in accordancewith the estimated position of the third survey station.
 5. The methodof claim 1, the method further comprising: applying corrections to theattitude of the second survey station based on drilling in accordancewith the estimated position of the third survey station.
 6. The methodof claim 1, wherein estimating the position of the third survey stationfurther comprises using supplemental information outside of stationarysurvey data.
 7. The method of claim 1, the method further comprising:after estimating the position of the third survey station, applying aminimum curvature solution to the first interval and the second intervalsuch that the first modeled well path and the second modeled well pathintersect at the second survey station.
 8. The method of claim 1,wherein a first measured depth of the first survey station is less thana second measured depth of the second survey station, and the secondmeasured depth is less than a third measured depth of the third surveystation.
 9. The method of claim 1, wherein the third survey station isone of a notional survey station, an actual survey station, or a plannedsurvey station according to a planned wellbore path.
 10. The method ofclaim 1, wherein the second positional vector of the wellbore at thesecond survey station is determined using a continuous survey method.11. The method of claim 1, wherein the second positional vector of thewellbore at the second survey station is determined using a slide sheetmethod.
 12. A non-transitory computer-readable medium comprisingprocessor-executable instructions configured to cause one or moreprocessors to: receive attitudes at a first survey station and a secondsurvey station along a wellbore path using a downhole surveying tool,wherein the first survey station and the second survey station areconsecutive; model, based on a first attitude of the wellbore at thefirst survey station, a first interval between the first survey stationand the second survey station as a first modeled well path; determine,based on the first modeled well path, a first positional vector of thewellbore at the first survey station; model, based on a second attitudeof the wellbore at the second survey station, a second interval betweenthe second survey station and an estimated position of a third surveystation as a second modeled well path; determine, based on the secondmodeled well path, a second positional vector of the wellbore at thesecond survey station; and estimate, a position of the third surveystation based on the first modeled well path, second modeled well path,first positional vector, and the second positional vector, wherein thethird survey station is beyond the second survey station along thewellbore path.
 13. The non-transitory computer-readable medium of claim12, wherein the one or more processors are configured to execute furtherprocessor-executable instructions stored in the non-transitorycomputer-readable medium to: determine a third attitude of the wellboreat the third survey station.
 14. The non-transitory computer-readablemedium of claim 13, wherein the one or more processors are configured toexecute further processor-executable instructions stored in thenon-transitory computer-readable medium to: set the third attitude to bethe same as a second attitude of the wellbore at the second surveystation.
 15. The non-transitory computer-readable medium of claim 12,wherein the one or more processors are configured to execute furtherprocessor-executable instructions stored in the non-transitorycomputer-readable medium to: drill in accordance with the estimatedposition of the third survey station.
 16. The non-transitorycomputer-readable medium of claim 12, wherein the one or more processorsare configured to execute further processor-executable instructionsstored in the non-transitory computer-readable medium to: applycorrections to the attitude of the second survey station based ondrilling in accordance with the estimated position of the third surveystation.
 17. The non-transitory computer-readable medium of claim 12,wherein instructions to estimate the position of the third surveystation further cause the one or more processors to execute furtherprocessor-executable instructions stored in the non-transitorycomputer-readable medium to: receive supplemental information outside ofstationary survey data; and estimate the position of the third surveystation based on the supplemental information.
 18. The non-transitorycomputer-readable medium of claim 12, wherein the one or more processorsare configured to execute further processor-executable instructionsstored in the non-transitory computer-readable medium to: afterestimating the position of the third survey station, apply a minimumcurvature solution to the first interval and the second interval suchthat the first modeled well path and the second modeled well pathintersect at the second survey station.
 19. The non-transitorycomputer-readable medium of claim 12, wherein a first measured depth ofthe first survey station is less than a second measured depth of thesecond survey station, and the second measured depth is less than athird measured depth of the third survey station.
 20. A method ofdrilling a wellbore to a target, comprising: measuring attitudes at twoadjacent survey stations along a wellbore using a downhole surveyingtool; determining an actual change in wellbore position over a surveyleg by linking the two adjacent survey stations with a first modeledwell path; and interpolating a notional survey station between the twoadjacent survey stations, the interpolating comprising computing anattitude of the notional survey station such that a second modeled wellpath intersects the first modeled well path linking the two adjacentsurvey stations and notional survey station reflect the determinedactual change in wellbore position over the survey leg.
 21. The methodof claim 20, wherein determining the actual change in wellbore positioncomprises determining the actual change using continuous surveymeasurements taken at least between the two adjacent survey stationsduring drilling of the wellbore.
 22. The method of claim 20, whereindetermining the actual change in wellbore position comprises determiningthe actual change using continuous inclination measurements taken atleast between the two adjacent survey stations during drilling of thewellbore.
 23. The method of claim 20, wherein determining the actualchange in wellbore position comprises determining the actual changeusing depths and toolface directions defining slide intervals duringdrilling of the wellbore.
 24. The method of claim 20, wherein the firstmodeled well path and the second modeled well path are circular arcscomputed by a minimum curvature method.